03962nam a22005415i 4500 978-3-031-73737-4 DE-He213 20251030113302.0 cr nn 008mamaa 241108s2024 sz | s |||| 0|eng d 9783031737374 978-3-031-73737-4 10.1007/978-3-031-73737-4 doi QA403-403.3 PBKD bicssc MAT034000 bisacsh PBKD thema Córdoba, Antonio. author. aut http://id.loc.gov/vocabulary/relators/aut 87174 Suprematism in Harmonic Analysis [electronic resource] / by Antonio Córdoba. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Birkhäuser, 2024. XXII, 259 p. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Progress in Mathematics, 2296-505X ; 356 Preface -- Notions and terminology -- 1. Seven mathematical haikus -- 2. All those rectangles -- 3. As a needle turn: Besicovitch or Kakeya sets -- 4. Translation invariant operators -- 5. The multiplier problem for the ball -- 6. The ball multiplier on mixed norm spaces -- 7. The Poisson summation formula -- 8. Encounters at the interface with number theory -- 9. Weyl sums and atomic energy oscillations -- Bibliography. This award-winning monograph explores advanced topics in harmonic analysis, addressing both classical and contemporary problems. Several connections to number theory, crystallography or atomic theory are also surveyed. The term “suprematism” refers to a certain geometric point of view underlying proofs and arguments. The opening of the book is dedicated to a few results, with short statements and proofs, that could be called “mathematical haikus”. Then, in the first part of the book, singular integrals beyond the classical Calderón-Zygmund theory, such as Vitali-type covering lemmas and estimates for the corresponding maximal operators, are explored. The exponential overlapping of parallelepipeds, the strong maximal function, and Zygmund's conjecture about monotonic bases are also covered. The core of this part is devoted to the Kakeya maximal function and its relation to the spherical summation of Fourier series and integrals. The two-dimensional case is well understood, but the case of higher dimensions still presents many open problems and conjectures. The chapters in the second part of the book treat questions at the interface of harmonic analysis and number theory, including applications of the Poisson summation formula to crystallography and arithmetic, estimates of the Minkowski dimension of Riemann graphs, random lattice point problems, and the role of Weyl sums in atomic energy oscillations. With a focus on rigorous research insights for graduate students and researchers in mathematics, this book provides a comprehensive journey through the hidden landscapes of harmonic analysis. Harmonic analysis. 72301 Functions of real variables. 83964 Fourier analysis. Abstract Harmonic Analysis. 72305 Real Functions. 83965 Fourier Analysis. SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031737367 Printed edition: 9783031737381 Printed edition: 9783031737398 Progress in Mathematics, 2296-505X ; 356 74786 https://doi.org/10.1007/978-3-031-73737-4 ZDB-2-SMA ZDB-2-SXMS 64790 64790